Harry Potter and the invisible horses

This has been bugging me. I've been re-reading the entire Harry Potter series since some time in February or March, and I've got three weeks to finish re-reading Half Blood Prince before the last one comes out.

If you are even remotely a fan, I highly recommend doing this, by the way. I read the first three books back in 2000 or so, and have read each subsequent one as it came out. (That and blogging may well have been the only two times in my life I was even incrementally ahead of the pop culture bandwagon instead of running behind it, begging to be let on.) Anyway, re-reading them has made me even more of a fan, and I'm going to be hugely disappointed when the last one is done and there's nothing left to anticipate.

But something is bugging me - well, aside from the central question around the ending of Half Blood Prince, which at least will likely be answered by the last book. But in the Order of the Phoenix, they have those flying skeletal horses - Thestrals? - that you can only see if you've witnessed death. Harry can see them by the beginning of the fifth book because he's witnessed Cedric's death in the Triwizard Tournament. But the central mythology around Harry is that when Voldemort tried to kill Harry his mother's love protected him, so Voldemort killed his parents instead. Wouldn't Harry have therefore witnessed his parents' death as well, especially since when he encounters the Dementors he talks about hearing his mother screaming? So hasn't he technically witnessed his parents' death as well?

This kind of things are keeping me up at night...